Question

The area Ar (in square meters) of a circular algae colony with radius r meters is given by =Arπr2. The radius Mt (in meters) after t minutes is given by =Mt103t. Write a formula for the area Zt (in square meters) of the algae colony after t minutes. It is not necessary to simplify.

Answer 1

Answer:

$Z(t)=\pi (\frac{10}{3}t)^2$

Step-by-step explanation:

We have been given that the area $A(r)$ (in square meters) of a circular algae colony with radius r meters is given by $A(r)=\pi r^2$. The radius $M(t)$ (in meters) after t minutes is given by $M(t)=\frac{10}{3}t$. We are asked to write the formula for the area $Z(t)$ (in square meters) of the algae colony after t minutes.  

This problem is based on composite functions, in which function $M(t)$ represents radius of circle after t minutes.

To write the formula for the area $Z(t)$ (in square meters) of the algae colony after t minutes, we need to substitute $r=\frac{10}{3}t$ in area formula $A(r)$.

$Z(t)=\pi (\frac{10}{3}t)^2$

Therefore, our required formula would be $Z(t)=\pi (\frac{10}{3}t)^2$.